Question

The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of 0.45 m and a speed of 3000 r.p.m. clockwise when looking from stern. Determine the gyroscopic couple upon the ship when the ship is pitching in a simple harmonic motion, the bow falling with its maximum velocity. The period of pitching is 40 seconds and the total angular displacement between the two extreme positions of pitching is 12 degrees.

(a) 3.675 kN-m

(b) 4.675 kN-m

(c) 5.675 kN-m

(d) 6.675 kN-m

This question was addressed to me during an internship interview.

The doubt is from Effect of Gyroscopic Couple on an Aeroplane in division Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

Correct answer is (a) 3.675 kN-m

To explain: Given: tp = 40 s

Since the total angular displacement between the two extreme positions of pitching is 12° (i.e. 2φ = 12°), therefore amplitude of swing,

φ = 12 / 2 = 6° = 6 × π/180 = 0.105 rad

and angular velocity of the simple harmonic motion,

ω1 = 2π / tp = 2π / 40 = 0.157 rad/s

We know that maximum angular velocity of precession,

ωp = φ.ω1 = 0.105 × 0.157 = 0.0165 rad/s

 Gyroscopic couple,

C = I.ω.ωp

  = 708.75 × 314.2 × 0.0165 = 3675 N-m

  = 3.675 kN-m